An adsorbed natural gas storing tank is provided. The adsorbed natural gas storing tank includes a tank body that has an upper plate and a lower plate coupled to define an inner space provided with an adsorbent material. The tank body includes an opening that extends through the upper and lower plates. A central plate is inserted in the opening to seal one side of the tank body. Additionally, the central plate has a plurality of discharge apertures formed along a circumferential wall thereof to discharge natural gas reacted with the adsorbent material and has a mounting region therein. A filter assembly is inserted in the mounting region, is fastened to the central plate, filters natural gas passing through the discharge apertures, and is equipped with a control valve for adjusting natural gas discharge.